Nyquista

Nyquista, a grinning goblin of the circuits, holds a striped resistor spitting jagged orange sparks.

The Physics

Any resistor at a temperature above absolute zero hisses with voltage noise, because its electrons jiggle thermally. John B. Johnson measured it at Bell Labs and Harry Nyquist explained it, both in 1928 (Phys. Rev. 32, 97 and 32, 110). The noise power per unit bandwidth depends only on temperature and resistance, not on the material.

⟨V²⟩ = 4k_BTRΔf

• ⟨V²⟩: mean-square noise voltage (V²)
• k_B: Boltzmann constant, exactly 1.380 649 × 10⁻²³ J/K since 2019
• T: temperature (K)
• R: resistance (Ω)
• Δf: measurement bandwidth (Hz)

A 1 kΩ resistor at room temperature gives about 4 nV per √Hz. Because k_B is now exact, Johnson noise can be used as a primary thermometer.

Honest caveat: The formula is the low-frequency limit; at very high frequency or low temperature quantum corrections (hf ≳ k_BT) cut it off.

On the sticker

Nyquista holds a striped resistor with jagged orange lightning crackling from it. Printed text: NYQUISTA with the line 4kTR. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.